Cosmology models with \Omega_M-dependent cosmological constant

We investigate the evolution of the scale factor in a cosmological model in which the cosmological constant is given by the scalar arisen by the contraction of the stress-energy tensor.Comment: 10 page

Quantum-information entropies for highly excited states of single-particle systems with power-type potentials

The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x^2k with k∈N and x∈R, is investigated in the position and momentum spaces within the semiclassical (WKB) approximation. It is found that for highly excited states both physical entropies, as well as their sum, have a logarithmic dependence on its quantum number not only when k=1 (harmonic oscillator), but also for any fixed k. As a by-product, the extremal case k→∞ (the infinite well potential) is also rigorously analyzed. It is shown that not only the position-space entropy has the same constant value for all quantum states, which is a known result, but also that the momentum-space entropy is constant for highly excited states

Notes on entropic characteristics of quantum channels

One of most important issues in quantum information theory concerns transmission of information through noisy quantum channels. We discuss few channel characteristics expressed by means of generalized entropies. Such characteristics can often be dealt in line with more usual treatment based on the von Neumann entropies. For any channel, we show that the $q$-average output entropy of degree $q\geq1$ is bounded from above by the $q$-entropy of the input density matrix. Concavity properties of the $(q,s)$-entropy exchange are considered. Fano type quantum bounds on the $(q,s)$-entropy exchange are derived. We also give upper bounds on the map $(q,s)$-entropies in terms of the output entropy, corresponding to the completely mixed input.Comment: 10 pages, no figures. The statement of Proposition 1 is explicitly illustrated with the depolarizing channel. The bibliography is extended and updated. More explanations. To be published in Cent. Eur. J. Phy

Galilean Transformation Expressed by the Dual Four-Component Numbers

We express the special Galilean transformation in the algebraic ring of the dual four-component numbers

Multicomponent Number Systems

We introduce three types of the four-component number systems which are constructed by joining the complex, binary and dual two-component numbers. We study their algebraic properties and rewrite the Euler and Moivre formulas for them. The most general multicomponent number system joining the complex, binary dual numbers is the eight-component number system, for which we determine the algebraic properties and the generalized Euler and Moivre formulas. Some applications of the multicomponent number systems in differential and integral calculus, which are of physical relevance, are also presented

Basic Space-Time Transformations Expressed by Means of Two-Component Number Systems

We slow that the Lorentz and Galilei transformations can be expressed in the algebraic structures called the rings of two-component binary and dual number systems